Pencil Polyhedra

After watching Little Man Tate, a movie about a child prodigy, I grabbed some pencils and elastics as he did and tried to make some geometric shapes. I made three of the five Platonic Solids;

the tetrahedron, with 6 pencils (edges) and 4 elastics (vertices),

Here's an 'imploded' version of the tetrahedron; the elastics have been moved much closer to the middle of the pencils.

the octahedron, with 12 pencils and 6 elastics,

and the icosahedron, with 30 pencils and 12 elastics.

The reason I only made 3 of the 5 platonic solids is because the other two are unstable. The icosahedron was very difficult while building, but once it was completed it was very stable. The cube on the other hand was frustrating the entire time. The dodecahedron was virtually impossible. This (in)stability has to do with the shapes of the faces. Notice that the three I made had all triangular faces. I explain this in detail here.

I tried to make a cube with hypotenuses as I mentioned. This has a few, but the pencil thickness starts becoming a large enough factor to cause distortion by itself. Also, the hypotenuse is longer than the edge, so I had to move the elastics closer to the middle of the pencils.

Lastly, I made some DNA. This is something I try with any modeling set I come across, e. g. Legos or Zome. The joint I used to attach here was a little ridiculous, but was the most stable thing I could come up with. It works perfectly fine if the DNA is infinitely long, otherwise you need to pull on it.


Overall this was very fun, and the first two structures were easy. Grab some pencils and elastics and see what you come up with.

-Alex Scott